The number of stock offerings of new companies will explode during 1985, predicts New Issues, a newsletter based in Fort Lauderdale.

During 1985's first quarter ended March 31, stock offerings of 98 companies raised $1.23 billion. That compares with stock offerings of 174 companies totaling $1.25 billion during 1984's first quarter.

Norman G. Fosback, editor of New Issues, predicts that by year's end the value of stock offerings will amount to $7 billion, surpassing 1984's $3.98 billion total.

If Fosback's predictions come true, 1985 would be the second biggest year for stock offerings. The record year was 1983 with a $12.95 billion total.

That fewer companies during 1985's first quarter could raise almost as much money as during the same period last year was the result of a few large deals, according to Fosback.

Some of the larger stock offerings earlier this year included $200 million for Gemini II, $171 million for EQK Equity Investors, $115 million for ICM Property Investors and $76 million for Herman's Sporting Goods.

In addition, stock prices are increasing, Fosback notes.

LSI Lighting's stock price per share increased to $17 from $12.50 during the first day of trading, March 12. Pasta & Cheese's stock price per share increased to $12 from $6 during the first day of trading, March 5.

LSI, which is based in Cincinnati, is a supplier of outdoor lighting to companies. Pasta & Cheese, which is based in Long Island City, N.Y., is a chain of retail food shops.

Of the 98 companies converting to public ownership during 1985's first quarter, five are based in Florida. They are: Business Computer Solutions in Coral Gables, Metalbanc in Miami, Penny Stock Investment Co. in Pompano Beach, Pioneer Savings Bank in Clearwater and Venus Cruise Lines in Cape Canaveral.

Stock prices overall will increase 15 percent this year, Fosback predicts. ''That kind of performance will in all likelihood lead to a veritable explosion in the new issues sector,'' he writes.

Because some measures of stock prices, such as the Dow Jones industrial average, set records early this year, public demand for new stock offerings will increase, he continues. In addition, many companies with plans to convert from private to public ownership have decided to test ''the equity waters,'' he concludes.

Fosback founded New Issues in 1978. The monthly newsletter highlights companies that are converting from private to public ownership through stock offerings. Going Public, which is based in Philadelphia, also keeps track of stock offerings.

In New Issues' most recent edition, Fosback provides investors with a way to determine whether a stock price is reasonable. He suggests that investors use a ''price-revenues ratio,'' which is the stock price per share divided by the revenue per share. A ratio of 2 is favorable and a ratio of 5 or more indicates risk, according to Fosback.

Offerings expected in April are varied. They include:

-- United States Basketball League Inc., which is raising $3.9 million through selling stocks and warrants.

The company, whose officers include former professional athletes Earl Monroe and Walt Frasier, plans to organize a professional summer basketball league. Divisions are planned for the East this year, the West next year and the Central United States in 1987.

United States Basketball League plans to sell franchises for $100,000 to $200,000 each.

-- Feyline Presents, one of the nation's biggest promoters of rock concerts. It is raising $4.7 million through selling stock.

The company's annual revenue is about $25 million from promoting such stars as Willie Nelson and Bruce Springsteen, and such events as symphony concerts. New Issues notes that Feyline Presents' public stockholders will own 49 percent of the company, while insiders will own 51 percent for a $470,000 investment.

Salaries and bonuses of top officers will be extremely generous, New Issues reports. ''It is difficult to see anything attractive in this offering to public stockholders.''

-- Airship International Ltd., which is raising $3 million to buy a helium blimp that is 193 feet long.

The aircraft will be used for advertising and promotions.

-- Rent-A-Wreck of America, which is raising $3 million to expand. The company, which already is publicly owned, has established 300 car rental franchises.

Rent-A-Wreck has a fleet of 7,500 cars, vans and trucks. The company charges lower rates because it reconditions used vehicles.

New Issues notes that profit growth has lagged revenue growth. Consequently, the stock price is too high for investors, the newsletter concludes.